As described in Japanese Patent Laid-open Publication No. 2001-159448, for example, an isolation damper pulley has a damper section attached to a crankshaft and an isolation pulley section assembled to the damper section. The damper section has a hub attached to the crankshaft and an annular mass body fixed to a cylindrical portion of the hub via an annular elastic member. The isolation pulley section includes: a pulley portion, which comprises a cylindrical portion having a pulley groove formed in its outer circumferential surface and a cover portion extending from one end of the cylindrical portion in a central direction thereof; and an annular elastic member whose one end is fixed to the cover portion, wherein the other end of the annular elastic member is fixed to the hub via a supporting member.